I would be concerned about the toxins being dumped. But I also would be worried about passing it on to the baby. I would recommend doing it, but easing in very slowly, and not doing any of the detoxing supplements. Coconut oil is very good for you, the baby, and for killing yeast. But, you will experience die off when taking it, so ease into it.
As far as what to do/not to do, think of it in terms of your general health. It's healthy to not eat grains, so no problem there. It's healthy to entirely cut out all sweets - no problem there. Fruits do not provide any additional nutrients that you can't get from eggs, meats, veggies, & healthy fats. Many candida diets cut out or restrict dairy. If you do that part, you'll have to replace the protein, calcium, & fat. (meats & eggs, broccoli & leafy greens, butter is okay, olive oil, coconut oil, & fats from meats are healthy.)
So from a nutritional standpoint, it's a healthy diet. The die-off/detoxing is the only part that you have to go slow with.
Oh, there is also controversy about putting your body into ketosis while pregnant. But you may not have that problem since you are going to ease your way into the diet. But do some research there to figure out your comfort level with that.